A2 Collaboration

The electric ($\alpha_{\text{E1}}$) and magnetic ($\beta_{\text{M1}}$) scalar polarizabilities describe the response of the nucleon to an applied electric or magnetic field. They are not only fundamental properties related to the internal structure and dynamics of the nucleon, but they are important also in other areas of physics, such as atomic structure. The values of $\alpha_{\text{E}1}$ and $\beta_{\text{M}1}$ quoted by the Particle Data Group were determined using data on the unpolarized differential cross-section of the Compton scattering $\gamma p \rightarrow \gamma p$. The measurement of the beam asymmetry $\Sigma_3$ provides an alternative approach to the extraction of the scalar polarizabilities, with different sensitivity and systematics compared to the unpolarized cross-section. This asymmetry was measured recently for the first time below the pion photoproduction threshold by the A2 Collaboration with the Crystal Ball/TAPS experiment at MAMI (Mainz, Germany). A linearly polarized photon beam impinged on a liquid hydrogen target and the scattered photons were detected with the Crystal Ball/TAPS setup, providing almost 4$\pi$ coverage.

A new high precision measurement of both a unpolarized cross-section and beam asymmetry $\Sigma_3$ is ongoing at MAMI and the polarizabilities $\alpha_{\text{E}1}$ and $\beta_{\text{M}1}$ will be extracted with unprecedented precision. The impact of the recently obtained and expected results on the extraction of the scalar polarizabilities will be discussed in this talk.

$^*$On behalf of the A2 Collaboration at MAMI.